Near misses: why a symbol just off the line counts for nothing

Four matching symbols on five reels and no payout feels like a spin that nearly worked. On a ways-to-win slot it can be a spin that was never close, because the evaluation reads reels in order and stops at the first reel without the symbol. This post explains that rule and works through an invented example. The odds below are made up for the arithmetic. They are not taken from Brasslight Slots or any real game, and the Play listing for that app states no symbol frequencies or pay table.

How a ways line is read

A 5-reel, 3-row slot with 243 ways to win has 3 × 3 × 3 × 3 × 3 = 3⁵ = 243 routes through the grid, one symbol per reel. The companion post on what 243 ways to win means covers the count. A way pays when it runs through adjacent reels from the left. Reel 1 must show the symbol, then reel 2, then reel 3, and so on. Rows do not matter; any of the three on each reel will do.

For the sums I assume the usual convention that a win needs the symbol on at least the first three reels in a row. Check that rule in any game you play, as this post does not claim it for a particular app. Wilds are left out to keep the numbers clean; the post on wilds on a ways slot shows how they change the count.

The consequence is that position matters more than quantity. A symbol on reels 1, 2, 4 and 5 is four symbols, but the run from the left ends at reel 2. Two reels is not enough, so the spin pays nothing. A symbol on reels 1, 2, 3 and 4 is also four symbols, and it pays.

An invented symbol

Suppose a symbol shows somewhere on a given reel (in at least one of its three rows) with probability 0.4, and that each reel is independent of the others. Both figures are assumptions. Independence is the same idea as in why a slot is never due: one reel's result tells you nothing about another's. So the chance of any particular pattern of hits and misses is a product.

The chance of a miss on a reel is 1 − 0.4 = 0.6. Take the pattern hit, hit, miss, hit, hit, written as reels 1 to 5:

0.4 × 0.4 × 0.6 × 0.4 × 0.4 = 0.4⁴ × 0.6 = 0.0256 × 0.6 = 0.01536, or 1.536%.

Every pattern with exactly four hits and one miss has the same four 0.4s and one 0.6, so each has the same chance, 1.536%, wherever the miss falls. There are five such patterns, which together make 5 × 1.536% = 7.68% of spins.

Which of the five pay

The same number of symbols gives very different results, depending on where the gap sits:

• Miss on reel 5 (hit, hit, hit, hit, miss): a four-reel run from the left. Pays.
• Miss on reel 4 (hit, hit, hit, miss, hit): a three-reel run. Pays.
• Miss on reel 3 (hit, hit, miss, hit, hit): a two-reel run. Pays nothing.
• Miss on reel 2 (hit, miss, hit, hit, hit): a one-reel run. Pays nothing.
• Miss on reel 1 (miss, hit, hit, hit, hit): no run, because reel 1 has none. Pays nothing.

Two of the five patterns pay, which is 2 × 1.536% = 3.072%. Three do not: 3 × 1.536% = 4.608%. So 60% of the four-symbol spins (3 of 5) pay nothing, and a screen that shows four of the symbol and no win is more common than one that shows four in a row from the left and pays for it. For comparison, all five reels hitting has chance 0.4⁵ = 0.01024, or 1.024%.

Stopping at two reels

A win of at least three reels needs hits on reels 1, 2 and 3: 0.4³ = 0.064, or 6.4% of spins. A run that stops at exactly two reels needs hits on reels 1 and 2 and a miss on reel 3: 0.4 × 0.4 × 0.6 = 0.096, or 9.6%. Under these assumptions a two-reel stop is more common than a payout, and whatever sits on reels 4 and 5 afterwards cannot change that.

Is a near miss a sign of anything?

No. Because the reels are independent in this model, the pattern on one spin has no effect on the next. After a four-symbol spin that paid nothing, the chance of a win on the following spin is still the same 6.4% as before. The spin did not move the game closer to a payout; there is no store of progress to move. A near miss is a description of how the symbols landed, and the evaluation rule decides whether it pays.

It is common to feel that such a spin means something. Players generally find a result that is close to a win more striking than one that is nowhere near. The feeling is real; the information is not there. If you want to judge a game, count how often a symbol pattern pays, not how it looks.

Checking it yourself

1. Pick a symbol and a hit chance. Use 0.4, or any figure you like. The shape of the result holds for any chance between 0 and 1.
2. Multiply along the reels. Hit chance for a hit, one minus it for a miss. Every four-hit pattern gives the same product.
3. Read from the left. Count the unbroken run from reel 1. Fewer than three reels pays nothing under the assumed rule.

Real games differ in reel layouts, wilds and minimum matches, and the Play listing for Brasslight Slots: Casino Games gives none of those details, so the figures above show how the reading works, not how often anything lands in the app.